Estimation of Number of Precipitate Particles per Unit Volume from Measurements on Polished Specimen Surfaces—Computer Simulation

Abstract

In studies of phase transformation kinetics a stereological analysis is often employed to determine the number of precipitate particles in the specimen volume from particle numbers measured on polished surfaces. Possible sources of error in applying Schwartz-Saltykov diameter analysis to measurements in actual microstructures were studied by computer simulation. Particles were generated in a fixed volume and their sizes were increased at prescribed nucleation and growth rates. The number and size distribution of sections were measured on random planes and the temporal variation of particle numbers per unit volume was calculated. It is demonstrated that the uncertainty of D_max, the maximum particle size to be determined from microstructure in each measurement, does not cause an appreciable amount of error if D_max is less than 3–5 times the actual maximum particle size. The increase in size and impingement of particles can produce a very different temporal variation of apparent particle numbers on the plane of polish from the variation of actual particle numbers in the specimen volume. The non-sphericity of particles, especially particles elongated in one direction ( e.g. prolate ellipsoids), may cause a significant amount of error if they are treated as spherical particles.